We consider the following method à la Nitsche to approximate problem (REF ), originally introduced in [1]}:
Find \(u_h\in V_h\)  such that
\(a(u_h,v_h)- \left(\left[P_{1,\gamma }^n(u_h)\right]_{\mathbb {R}^-}, v_h^n \right)_{\Gamma _C}= L(v_h) \qquad \forall v_h\in V_h.\) 
